Fig. 2.

(A) Simulated 2D morphospace of equal-volume body shapes. Empty region at upper left consists of nonphysical self-intersecting shapes. (B) Example body + flagellum with simulated swimming trajectory traced by the body midpoint, which appears to lack any symmetry viewed off-axis but reveals long-range rotational symmetry viewed axially (Inset). (C) The random Brownian rotation that would be superimposed onto the swimming trajectory can be quantified by three anisotropic rotational diffusivities, depicted as circles with diameter proportional to diffusivity. These rotations occur around principal axes (light gray lines) passing through the center of diffusion (black circle) (30). The largest of these (dashed) corresponds to rotations around an axis close to the flagellar axis, but it is the other two (solid) that determine how long the cell can maintain its course. (D) Comparison of optimal flagellar shapes for a sphere ($\mathrm{ℒ}=1$, $\mathcal{K}=0$) and highly elongated curved rod ($\mathrm{ℒ}=10$, $\mathcal{K}=0.5$), for Swimming Efficiency (red) and Chemotactic SNR (blue). Example second-order triangular surface meshes are shown in B–D; the flagella were similarly fully meshed (SI Appendix, section 5).